whitney-trick-opposite-sign-double-points-disc
IN premise — summaries/2026/08/24/wiki-Whitney_embedding_theorem.md
Created 2026-08-24T17:11:28+00:00
The Whitney Trick eliminates a pair of opposite-sign double points on an immersed manifold by constructing an embedded disc between them and pushing the manifold across the disc via a 1-parameter family of immersions.
Summary
When a surface (or higher-dimensional shape) crosses itself at two points in a compatible, opposite way, those two self-intersections can be erased in one move by sliding the surface across a disk that connects them. This is a trusted foundational tool the system can build on: it tells us which kinds of self-intersections are fixable and therefore should not affect the true shape or classification of the object.